More particularly, this device is of the type of those known to the prior art, in which the axle of the crank drive is provided with a stationary pinion, connected by an endless chain, to the free-wheel pinion secured to the back wheel of the moped for driving this wheel by pedaling. Furthermore, the axle of the crank drive freely passes through the hub of a pulley, having a trapezoidal groove, which is connected by an endless belt to a drive pulley driven by the engine. The device further includes a hub, on which is mounted to freely rotate, a double pinion, one of the gears of which is engaged with an endless chain connecting it to a gear which is integral with the back wheel of the moped and another gear of which works in conjunction with a mechanism carried by said grooved pulley, thus making it possible, at will, to connect or disconnect this pulley with said double pinion.